x^3(sinx)/ 5cosx
To simplify the expression (x^3*sin(x))/(5*cos(x)), we can divide the numerator and denominator separately.
Step 1: Divide the numerator, x^3*sin(x), by the denominator, 5*cos(x), separately.
Step 2: Simplify the numerator.
The numerator, x^3*sin(x), cannot be simplified further.
Step 3: Simplify the denominator.
The denominator, 5*cos(x), cannot be simplified further.
So, the simplified expression is (x^3*sin(x))/(5*cos(x)).
To evaluate the expression x^3(sinx)/ 5cosx, we can follow these steps:
Step 1: Simplify the expression.
Write the expression as (x^3 * sinx) / (5 * cosx).
Step 2: Apply trigonometric identities and simplify further.
Recall the identity: sinx / cosx = tanx.
Now we can rewrite the expression as (x^3 * sinx) / (5 * cosx) = x^3 * (sinx / cosx) / 5.
Replacing sinx / cosx with tanx, we get x^3 * tanx / 5.
Step 3: Answer the expression.
So, the final simplified expression is x^3 * tanx / 5.
Note: It is important to be aware of any restrictions on the domain of the function when dealing with trigonometric functions, such as avoiding division by zero for cosx.